A gallery of seed profiles is constructed and the initial parameter values associated
with the profiles are selected using manufacturing process knowledge of semiconductor
devices. Manufacturing process knowledge may also be used to select the best seed
profile and the best set of initial parameter values as the starting point of an
optimization process whereby data associated with parameter values of the profile
predicted by a model is compared to measured data in order to arrive at values
of the parameters. Film layers over or under the periodic structure may also be
taken into account. Different radiation parameters such as the reflectivities RS,
RP and ellipsometric parameters may be used in measuring the diffracting
structures and the associated films. Some of the radiation parameters may be more
sensitive to a change in the parameter value of the profile or of the films then
other radiation parameters. One or more radiation parameters that are more sensitive
to such changes may be selected in the above-described optimization process to
arrive at a more accurate measurement. The above-described techniques may be supplied
to a track/stepper and etcher to control the lithographic and etching processes
in order to compensate for any errors in the profile parameters.